To determine the equation of a line that passes through the point [tex]\((3,2)\)[/tex] and is parallel to the [tex]\( y \)[/tex]-axis, let's carefully think through the properties of such lines.
### Step-by-Step Solution
1. Understanding the Properties of Lines Parallel to the [tex]\( y \)[/tex]-axis:
- A line that is parallel to the [tex]\( y \)[/tex]-axis has a constant [tex]\( x \)[/tex]-coordinate for all points on the line. This means that no matter what the [tex]\( y \)[/tex]-coordinate is, the [tex]\( x \)[/tex]-coordinate does not change.
2. Given Point:
- The line must pass through the point [tex]\((3,2)\)[/tex].
3. Determining the Constant [tex]\( x \)[/tex]-Value:
- Since the line is parallel to the [tex]\( y \)[/tex]-axis, it must have a constant [tex]\( x \)[/tex]-value. Given the point has an [tex]\( x \)[/tex]-value of 3, the equation will be of the form [tex]\( x = 3 \)[/tex].
4. Conclusion:
- The correct equation of the line is [tex]\( x = 3 \)[/tex].
### Answer Verification:
Let's double-check by considering the point and ensuring it fits the equation [tex]\( x = 3 \)[/tex]. For the point [tex]\((3,2)\)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex]:
- It satisfies the given point because [tex]\( x \)[/tex] is indeed 3.
### Final Answer:
B. [tex]\( x=3 \)[/tex]
